I would bet that cooking on the offset made the biggest smoke flavor difference. Three chunks and some charcoal can be plenty of smoke flavor in a Weber, but on an offset, you need to keep feeding sticks of wood. Keep trying. I bet that once you get your technique/ procedures dialed in, you will get the flavors that you are looking for.
18.5 WSM, Green Weber Genesis320, Cast iron firepit(w/grill), and a Copper Weber 22" OTS